LMFDB - Embedded newform 729.2.g.b.109.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(28,729)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([44]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("729.28");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.g (of order $27$, degree $18$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$8$ over $\Q(\zeta_{27})$
Twist minimal:	no (minimal twist has level 81)
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			109.4
Character	$\chi$	$=$	729.109
Dual form			729.2.g.b.622.4

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.209640 - 0.222205i) q^{2} +(0.110863 - 1.90345i) q^{4} +(-2.61158 + 0.305250i) q^{5} +(3.25303 + 1.63373i) q^{7} +(-0.914234 + 0.767134i) q^{8} +O(q^{10})$	\(q+(-0.209640 - 0.222205i) q^{2} +(0.110863 - 1.90345i) q^{4} +(-2.61158 + 0.305250i) q^{5} +(3.25303 + 1.63373i) q^{7} +(-0.914234 + 0.767134i) q^{8} +(0.615319 + 0.516314i) q^{10} +(0.993292 + 2.30271i) q^{11} +(3.58046 + 0.848584i) q^{13} +(-0.318940 - 1.06533i) q^{14} +(-3.42545 - 0.400377i) q^{16} +(0.339876 - 1.92753i) q^{17} +(0.311537 + 1.76682i) q^{19} +(0.291500 + 5.00486i) q^{20} +(0.303440 - 0.703454i) q^{22} +(7.59313 - 3.81342i) q^{23} +(1.86197 - 0.441294i) q^{25} +(-0.562046 - 0.973492i) q^{26} +(3.47037 - 6.01086i) q^{28} +(-0.589089 + 1.96770i) q^{29} +(-1.09276 - 0.718719i) q^{31} +(2.05450 + 2.75967i) q^{32} +(-0.499558 + 0.328565i) q^{34} +(-8.99425 - 3.27364i) q^{35} +(4.98391 - 1.81400i) q^{37} +(0.327285 - 0.439620i) q^{38} +(2.15343 - 2.28250i) q^{40} +(4.33403 - 4.59381i) q^{41} +(6.02768 - 8.09658i) q^{43} +(4.49321 - 1.63540i) q^{44} +(-2.43918 - 0.887789i) q^{46} +(7.71104 - 5.07163i) q^{47} +(3.73300 + 5.01429i) q^{49} +(-0.488400 - 0.321226i) q^{50} +(2.01218 - 6.72114i) q^{52} +(-6.60535 + 11.4408i) q^{53} +(-3.29697 - 5.71052i) q^{55} +(-4.22732 + 1.00189i) q^{56} +(0.560728 - 0.281608i) q^{58} +(0.370314 - 0.858484i) q^{59} +(0.114814 + 1.97128i) q^{61} +(0.0693827 + 0.393489i) q^{62} +(-1.01524 + 5.75769i) q^{64} +(-9.60969 - 1.12321i) q^{65} +(-1.71264 - 5.72061i) q^{67} +(-3.63128 - 0.860629i) q^{68} +(1.15813 + 2.68485i) q^{70} +(-4.97716 - 4.17634i) q^{71} +(-5.04878 + 4.23643i) q^{73} +(-1.44790 - 0.727165i) q^{74} +(3.39758 - 0.397121i) q^{76} +(-0.530804 + 9.11355i) q^{77} +(7.97870 + 8.45693i) q^{79} +9.06806 q^{80} -1.92935 q^{82} +(11.7053 + 12.4069i) q^{83} +(-0.299234 + 5.13765i) q^{85} +(-3.06274 + 0.357983i) q^{86} +(-2.67459 - 1.34323i) q^{88} +(3.64757 - 3.06067i) q^{89} +(10.2610 + 8.60997i) q^{91} +(-6.41685 - 14.8759i) q^{92} +(-2.74348 - 0.650217i) q^{94} +(-1.35293 - 4.51909i) q^{95} +(-9.02241 - 1.05457i) q^{97} +(0.331615 - 1.88068i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8}+O(q^{10}) $ 144 * q - 9 * q^2 + 9 * q^4 - 9 * q^5 + 9 * q^7 + 18 * q^8	$ 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8} - 18 q^{10} - 9 q^{11} + 9 q^{13} - 9 q^{14} + 9 q^{16} + 18 q^{17} - 18 q^{19} + 63 q^{20} + 9 q^{22} - 36 q^{23} + 9 q^{25} - 45 q^{26} - 9 q^{28} + 45 q^{29} + 9 q^{31} - 63 q^{32} + 9 q^{34} - 9 q^{35} - 18 q^{37} + 9 q^{38} + 9 q^{40} + 27 q^{41} + 9 q^{43} - 54 q^{44} - 18 q^{46} - 63 q^{47} + 9 q^{49} + 225 q^{50} + 27 q^{52} - 45 q^{53} - 9 q^{55} - 99 q^{56} + 9 q^{58} + 117 q^{59} + 9 q^{61} - 81 q^{62} - 18 q^{64} - 81 q^{65} + 36 q^{67} + 18 q^{68} + 63 q^{70} + 90 q^{71} - 18 q^{73} - 81 q^{74} + 90 q^{76} - 81 q^{77} + 63 q^{79} + 288 q^{80} - 36 q^{82} - 45 q^{83} + 63 q^{85} - 81 q^{86} + 90 q^{88} + 81 q^{89} - 18 q^{91} + 63 q^{92} + 63 q^{94} - 153 q^{95} + 36 q^{97} - 81 q^{98}+O(q^{100}) $ 144 * q - 9 * q^2 + 9 * q^4 - 9 * q^5 + 9 * q^7 + 18 * q^8 - 18 * q^10 - 9 * q^11 + 9 * q^13 - 9 * q^14 + 9 * q^16 + 18 * q^17 - 18 * q^19 + 63 * q^20 + 9 * q^22 - 36 * q^23 + 9 * q^25 - 45 * q^26 - 9 * q^28 + 45 * q^29 + 9 * q^31 - 63 * q^32 + 9 * q^34 - 9 * q^35 - 18 * q^37 + 9 * q^38 + 9 * q^40 + 27 * q^41 + 9 * q^43 - 54 * q^44 - 18 * q^46 - 63 * q^47 + 9 * q^49 + 225 * q^50 + 27 * q^52 - 45 * q^53 - 9 * q^55 - 99 * q^56 + 9 * q^58 + 117 * q^59 + 9 * q^61 - 81 * q^62 - 18 * q^64 - 81 * q^65 + 36 * q^67 + 18 * q^68 + 63 * q^70 + 90 * q^71 - 18 * q^73 - 81 * q^74 + 90 * q^76 - 81 * q^77 + 63 * q^79 + 288 * q^80 - 36 * q^82 - 45 * q^83 + 63 * q^85 - 81 * q^86 + 90 * q^88 + 81 * q^89 - 18 * q^91 + 63 * q^92 + 63 * q^94 - 153 * q^95 + 36 * q^97 - 81 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{7}{27}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.209640	−	0.222205i	−0.148238	−	0.157123i	0.649000	−	0.760789i	$-0.275188\pi$
$2$	−0.209640	−	0.222205i	−0.148238	−	0.157123i	−0.797237	+	0.603666i	$0.793706\pi$
$3$		0			0
$3$		0			0
$4$	0.110863	−	1.90345i	0.0554317	−	0.951725i
$5$	−2.61158	+	0.305250i	−1.16794	+	0.136512i	−0.677876	−	0.735177i	$-0.737099\pi$
$5$	−2.61158	+	0.305250i	−1.16794	+	0.136512i	−0.490060	+	0.871689i	$0.663025\pi$
$6$		0			0
$7$	3.25303	+	1.63373i	1.22953	+	0.617493i	0.940489	−	0.339824i	$-0.110368\pi$
$7$	3.25303	+	1.63373i	1.22953	+	0.617493i	0.289040	+	0.957317i	$0.406664\pi$
$8$	−0.914234	+	0.767134i	−0.323231	+	0.271223i
$9$		0			0
$10$	0.615319	+	0.516314i	0.194581	+	0.163273i
$11$	0.993292	+	2.30271i	0.299489	+	0.694293i	0.999809	−	0.0195355i	$-0.00621873\pi$
$11$	0.993292	+	2.30271i	0.299489	+	0.694293i	−0.700320	+	0.713829i	$0.746959\pi$
$12$		0			0
$13$	3.58046	+	0.848584i	0.993040	+	0.235355i	0.694852	−	0.719152i	$-0.255470\pi$
$13$	3.58046	+	0.848584i	0.993040	+	0.235355i	0.298188	+	0.954507i	$0.403618\pi$
$14$	−0.318940	−	1.06533i	−0.0852403	−	0.284722i
$15$		0			0
$16$	−3.42545	−	0.400377i	−0.856362	−	0.100094i
$17$	0.339876	−	1.92753i	0.0824319	−	0.467495i	−0.915449	−	0.402433i	$-0.868165\pi$
$17$	0.339876	−	1.92753i	0.0824319	−	0.467495i	0.997881	−	0.0650615i	$-0.0207243\pi$
$18$		0			0
$19$	0.311537	+	1.76682i	0.0714716	+	0.405335i	0.999464	+	0.0327364i	$0.0104222\pi$
$19$	0.311537	+	1.76682i	0.0714716	+	0.405335i	−0.927992	+	0.372599i	$0.878467\pi$
$20$	0.291500	+	5.00486i	0.0651814	+	1.11912i
$21$		0			0
$22$	0.303440	−	0.703454i	0.0646937	−	0.149977i
$23$	7.59313	−	3.81342i	1.58328	−	0.795152i	0.583423	−	0.812169i	$-0.301713\pi$
$23$	7.59313	−	3.81342i	1.58328	−	0.795152i	0.999855	+	0.0170164i	$0.00541675\pi$
$24$		0			0
$25$	1.86197	−	0.441294i	0.372393	−	0.0882589i
$26$	−0.562046	−	0.973492i	−0.110226	−	0.190917i
$27$		0			0
$28$	3.47037	−	6.01086i	0.655838	−	1.13595i
$29$	−0.589089	+	1.96770i	−0.109391	+	0.365392i	−0.995103	−	0.0988436i	$-0.968486\pi$
$29$	−0.589089	+	1.96770i	−0.109391	+	0.365392i	0.885712	+	0.464235i	$0.153671\pi$
$30$		0			0
$31$	−1.09276	−	0.718719i	−0.196265	−	0.129086i	0.447573	−	0.894248i	$-0.352289\pi$
$31$	−1.09276	−	0.718719i	−0.196265	−	0.129086i	−0.643838	+	0.765162i	$0.722659\pi$
$32$	2.05450	+	2.75967i	0.363188	+	0.487846i
$33$		0			0
$34$	−0.499558	+	0.328565i	−0.0856735	+	0.0563484i
$35$	−8.99425	−	3.27364i	−1.52031	−	0.553346i
$36$		0			0
$37$	4.98391	−	1.81400i	0.819351	−	0.298219i	0.101870	−	0.994798i	$-0.467517\pi$
$37$	4.98391	−	1.81400i	0.819351	−	0.298219i	0.717481	+	0.696579i	$0.245295\pi$
$38$	0.327285	−	0.439620i	0.0530926	−	0.0713157i
$39$		0			0
$40$	2.15343	−	2.28250i	0.340487	−	0.360896i
$41$	4.33403	−	4.59381i	0.676862	−	0.717432i	−0.294337	−	0.955702i	$-0.595099\pi$
$41$	4.33403	−	4.59381i	0.676862	−	0.717432i	0.971199	+	0.238270i	$0.0765802\pi$
$42$		0			0
$43$	6.02768	−	8.09658i	0.919213	−	1.23472i	−0.0525162	−	0.998620i	$-0.516724\pi$
$43$	6.02768	−	8.09658i	0.919213	−	1.23472i	0.971729	−	0.236097i	$-0.0758685\pi$
$44$	4.49321	−	1.63540i	0.677378	−	0.246545i
$45$		0			0
$46$	−2.43918	−	0.887789i	−0.359638	−	0.130897i
$47$	7.71104	−	5.07163i	1.12477	−	0.739773i	0.156006	−	0.987756i	$-0.450138\pi$
$47$	7.71104	−	5.07163i	1.12477	−	0.739773i	0.968764	+	0.247983i	$0.0797677\pi$
$48$		0			0
$49$	3.73300	+	5.01429i	0.533286	+	0.716327i
$50$	−0.488400	−	0.321226i	−0.0690702	−	0.0454282i
$51$		0			0
$52$	2.01218	−	6.72114i	0.279039	−	0.932055i
$53$	−6.60535	+	11.4408i	−0.907314	+	1.57151i	−0.0895334	+	0.995984i	$0.528538\pi$
$53$	−6.60535	+	11.4408i	−0.907314	+	1.57151i	−0.817781	+	0.575530i	$0.804796\pi$
$54$		0			0
$55$	−3.29697	−	5.71052i	−0.444563	−	0.770006i
$56$	−4.22732	+	1.00189i	−0.564900	+	0.133884i
$57$		0			0
$58$	0.560728	−	0.281608i	0.0736272	−	0.0369770i
$59$	0.370314	−	0.858484i	0.0482107	−	0.111765i	−0.892409	−	0.451228i	$-0.850986\pi$
$59$	0.370314	−	0.858484i	0.0482107	−	0.111765i	0.940619	+	0.339463i	$0.110245\pi$
$60$		0			0
$61$	0.114814	+	1.97128i	0.0147004	+	0.252397i	0.997650	+	0.0685200i	$0.0218277\pi$
$61$	0.114814	+	1.97128i	0.0147004	+	0.252397i	−0.982949	+	0.183877i	$0.941135\pi$
$62$	0.0693827	+	0.393489i	0.00881161	+	0.0499731i
$63$		0			0
$64$	−1.01524	+	5.75769i	−0.126904	+	0.719711i
$65$	−9.60969	−	1.12321i	−1.19194	−	0.139317i
$66$		0			0
$67$	−1.71264	−	5.72061i	−0.209232	−	0.698884i	−0.996599	−	0.0823999i	$-0.973742\pi$
$67$	−1.71264	−	5.72061i	−0.209232	−	0.698884i	0.787367	−	0.616484i	$-0.211444\pi$
$68$	−3.63128	−	0.860629i	−0.440357	−	0.104367i
$69$		0			0
$70$	1.15813	+	2.68485i	0.138423	+	0.320901i
$71$	−4.97716	−	4.17634i	−0.590681	−	0.495640i	0.297754	−	0.954643i	$-0.403762\pi$
$71$	−4.97716	−	4.17634i	−0.590681	−	0.495640i	−0.888435	+	0.459003i	$0.848207\pi$
$72$		0			0
$73$	−5.04878	+	4.23643i	−0.590915	+	0.495837i	−0.888511	−	0.458855i	$-0.848260\pi$
$73$	−5.04878	+	4.23643i	−0.590915	+	0.495837i	0.297596	+	0.954692i	$0.403815\pi$
$74$	−1.44790	−	0.727165i	−0.168316	−	0.0845312i
$75$		0			0
$76$	3.39758	−	0.397121i	0.389730	−	0.0455529i
$77$	−0.530804	+	9.11355i	−0.0604907	+	1.03859i
$78$		0			0
$79$	7.97870	+	8.45693i	0.897674	+	0.951479i	0.999059	−	0.0433680i	$-0.0138088\pi$
$79$	7.97870	+	8.45693i	0.897674	+	0.951479i	−0.101385	+	0.994847i	$0.532327\pi$
$80$	9.06806			1.01384
$81$		0			0
$82$	−1.92935			−0.213061
$83$	11.7053	+	12.4069i	1.28482	+	1.36183i	0.898195	+	0.439597i	$0.144879\pi$
$83$	11.7053	+	12.4069i	1.28482	+	1.36183i	0.386628	+	0.922236i	$0.373640\pi$
$84$		0			0
$85$	−0.299234	+	5.13765i	−0.0324565	+	0.557257i
$86$	−3.06274	+	0.357983i	−0.330264	+	0.0386023i
$87$		0			0
$88$	−2.67459	−	1.34323i	−0.285112	−	0.143189i
$89$	3.64757	−	3.06067i	0.386641	−	0.324430i	−0.428662	−	0.903465i	$-0.641015\pi$
$89$	3.64757	−	3.06067i	0.386641	−	0.324430i	0.815303	+	0.579035i	$0.196570\pi$
$90$		0			0
$91$	10.2610	+	8.60997i	1.07564	+	0.902570i
$92$	−6.41685	−	14.8759i	−0.669003	−	1.55092i
$93$		0			0
$94$	−2.74348	−	0.650217i	−0.282968	−	0.0670647i
$95$	−1.35293	−	4.51909i	−0.138807	−	0.463649i
$96$		0			0
$97$	−9.02241	−	1.05457i	−0.916087	−	0.107075i	−0.355032	−	0.934854i	$-0.615530\pi$
$97$	−9.02241	−	1.05457i	−0.916087	−	0.107075i	−0.561055	+	0.827779i	$0.689604\pi$
$98$	0.331615	−	1.88068i	0.0334982	−	0.189978i
$99$		0			0
$100$	−0.633558	−	3.59309i	−0.0633558	−	0.359309i
$101$	0.00860629	+	0.147764i	0.000856358	+	0.0147031i	0.998709	−	0.0507917i	$-0.0161745\pi$
$101$	0.00860629	+	0.147764i	0.000856358	+	0.0147031i	−0.997853	+	0.0654948i	$0.979137\pi$
$102$		0			0
$103$	−5.40424	+	12.5284i	−0.532495	+	1.23446i	0.413566	+	0.910474i	$0.364283\pi$
$103$	−5.40424	+	12.5284i	−0.532495	+	1.23446i	−0.946061	+	0.323989i	$0.894976\pi$
$104$	−3.92435	+	1.97088i	−0.384815	+	0.193261i
$105$		0			0
$106$	3.92694	−	0.930703i	0.381418	−	0.0903978i
$107$	0.424082	+	0.734532i	0.0409976	+	0.0710098i	0.885796	−	0.464075i	$-0.153613\pi$
$107$	0.424082	+	0.734532i	0.0409976	+	0.0710098i	−0.844799	+	0.535085i	$0.820280\pi$
$108$		0			0
$109$	−2.42376	+	4.19808i	−0.232154	+	0.402103i	−0.958442	−	0.285288i	$-0.907911\pi$
$109$	−2.42376	+	4.19808i	−0.232154	+	0.402103i	0.726288	+	0.687391i	$0.241244\pi$
$110$	−0.577730	+	1.92975i	−0.0550844	+	0.183995i
$111$		0			0
$112$	−10.4890	−	6.89870i	−0.991114	−	0.651866i
$113$	−5.46439	−	7.33995i	−0.514046	−	0.690484i	0.467000	−	0.884257i	$-0.345335\pi$
$113$	−5.46439	−	7.33995i	−0.514046	−	0.690484i	−0.981046	+	0.193773i	$0.937927\pi$
$114$		0			0
$115$	−18.6661	+	12.2769i	−1.74062	+	1.14482i
$116$	3.68010	+	1.33945i	0.341689	+	0.124365i
$117$		0			0
$118$	−0.268392	+	0.0976866i	−0.0247075	+	0.00899278i
$119$	4.25469	−	5.71504i	0.390027	−	0.523897i
$120$		0			0
$121$	3.23281	−	3.42658i	0.293892	−	0.311507i
$122$	0.413959	−	0.438771i	0.0374781	−	0.0397244i
$123$		0			0
$124$	−1.48919	+	2.00033i	−0.133734	+	0.179635i
$125$	7.62598	−	2.77563i	0.682089	−	0.248260i
$126$		0			0
$127$	−0.721881	−	0.262743i	−0.0640566	−	0.0233147i	0.309793	−	0.950804i	$-0.399740\pi$
$127$	−0.721881	−	0.262743i	−0.0640566	−	0.0233147i	−0.373850	+	0.927489i	$0.621962\pi$
$128$	7.24114	−	4.76257i	0.640033	−	0.420956i
$129$		0			0
$130$	1.76499	+	2.37079i	0.154800	+	0.207932i
$131$	6.76737	+	4.45097i	0.591268	+	0.388883i	0.809592	−	0.586993i	$-0.199689\pi$
$131$	6.76737	+	4.45097i	0.591268	+	0.388883i	−0.218324	+	0.975876i	$0.570059\pi$
$132$		0			0
$133$	−1.87306	+	6.25647i	−0.162415	+	0.542505i
$134$	−0.912112	+	1.57982i	−0.0787945	+	0.136476i
$135$		0			0
$136$	1.16795	+	2.02294i	0.100151	+	0.173466i
$137$	−8.98007	+	2.12831i	−0.767219	+	0.181834i	−0.595547	−	0.803320i	$-0.703065\pi$
$137$	−8.98007	+	2.12831i	−0.767219	+	0.181834i	−0.171671	+	0.985154i	$0.554917\pi$
$138$		0			0
$139$	−8.93500	+	4.48733i	−0.757857	+	0.380610i	−0.785382	−	0.619011i	$-0.787534\pi$
$139$	−8.93500	+	4.48733i	−0.757857	+	0.380610i	0.0275254	+	0.999621i	$0.491237\pi$
$140$	−7.22834	+	16.7572i	−0.610907	+	1.41624i
$141$		0			0
$142$	0.115408	+	1.98148i	0.00968481	+	0.166282i
$143$	1.60240	+	9.08765i	0.133999	+	0.759947i
$144$		0			0
$145$	0.937816	−	5.31862i	0.0778814	−	0.441687i
$146$	1.99978	+	0.233741i	0.165503	+	0.0193445i
$147$		0			0
$148$	−2.90032	−	9.68774i	−0.238405	−	0.796327i
$149$	1.59949	+	0.379087i	0.131036	+	0.0310560i	0.295610	−	0.955309i	$-0.404477\pi$
$149$	1.59949	+	0.379087i	0.131036	+	0.0310560i	−0.164575	+	0.986365i	$0.552625\pi$
$150$		0			0
$151$	−5.90832	−	13.6970i	−0.480812	−	1.11465i	−0.970139	−	0.242548i	$-0.922017\pi$
$151$	−5.90832	−	13.6970i	−0.480812	−	1.11465i	0.489327	−	0.872100i	$-0.337242\pi$
$152$	−1.64020	−	1.37629i	−0.133038	−	0.111632i
$153$		0			0
$154$	2.13635	−	1.79261i	0.172152	−	0.144453i
$155$	3.07322	+	1.54343i	0.246847	+	0.123971i
$156$		0			0
$157$	0.269384	−	0.0314865i	0.0214992	−	0.00251290i	−0.105337	−	0.994437i	$-0.533592\pi$
$157$	0.269384	−	0.0314865i	0.0214992	−	0.00251290i	0.126836	+	0.991924i	$0.459518\pi$
$158$	0.206520	−	3.54582i	0.0164299	−	0.282090i
$159$		0			0
$160$	−6.20789	−	6.57998i	−0.490777	−	0.520193i
$161$	30.9308			2.43769
$162$		0			0
$163$	−1.95301			−0.152972			−0.0764858	−	0.997071i	$-0.524370\pi$
$163$	−1.95301			−0.152972			−0.0764858	+	0.997071i	$0.524370\pi$
$164$	−8.26360	−	8.75890i	−0.645278	−	0.683955i
$165$		0			0
$166$	0.302979	−	5.20195i	0.0235157	−	0.403750i
$167$	−7.60986	+	0.889465i	−0.588869	+	0.0688289i	−0.405309	−	0.914180i	$-0.632836\pi$
$167$	−7.60986	+	0.889465i	−0.588869	+	0.0688289i	−0.183560	+	0.983009i	$0.558762\pi$
$168$		0			0
$169$	0.482351	+	0.242246i	0.0371039	+	0.0186343i
$170$	1.20434	−	1.01056i	0.0923689	−	0.0775067i
$171$		0			0
$172$	−14.7432	−	12.3710i	−1.12416	−	0.943281i
$173$	2.39938	+	5.56239i	0.182422	+	0.422901i	0.984748	−	0.173984i	$-0.0556641\pi$
$173$	2.39938	+	5.56239i	0.182422	+	0.422901i	−0.802327	+	0.596885i	$0.796405\pi$
$174$		0			0
$175$	6.77799	+	1.60641i	0.512368	+	0.121433i
$176$	−2.48052	−	8.28550i	−0.186976	−	0.624543i
$177$		0			0
$178$	−1.44477	−	0.168869i	−0.108290	−	0.0126573i
$179$	−0.479893	+	2.72161i	−0.0358689	+	0.203423i	−0.997476	−	0.0710082i	$-0.977378\pi$
$179$	−0.479893	+	2.72161i	−0.0358689	+	0.203423i	0.961607	+	0.274431i	$0.0884895\pi$
$180$		0			0
$181$	1.53100	+	8.68276i	0.113799	+	0.645384i	0.987338	+	0.158631i	$0.0507080\pi$
$181$	1.53100	+	8.68276i	0.113799	+	0.645384i	−0.873539	+	0.486754i	$0.838181\pi$
$182$	−0.237926	−	4.08503i	−0.0176362	−	0.302803i
$183$		0			0
$184$	−4.01651	+	9.31131i	−0.296101	+	0.686439i
$185$	−12.4622	+	6.25875i	−0.916238	+	0.460152i
$186$		0			0
$187$	4.77614	−	1.13197i	0.349266	−	0.0827775i
$188$	−8.79872	−	15.2398i	−0.641713	−	1.11148i
$189$		0			0
$190$	−0.720537	+	1.24801i	−0.0522733	+	0.0905400i
$191$	0.531278	−	1.77459i	0.0384419	−	0.128405i	−0.936615	−	0.350361i	$-0.886059\pi$
$191$	0.531278	−	1.77459i	0.0384419	−	0.128405i	0.975057	+	0.221956i	$0.0712441\pi$
$192$		0			0
$193$	−0.288860	−	0.189986i	−0.0207926	−	0.0136755i	0.539070	−	0.842261i	$-0.318776\pi$
$193$	−0.288860	−	0.189986i	−0.0207926	−	0.0136755i	−0.559863	+	0.828585i	$0.689146\pi$
$194$	1.65712	+	2.22590i	0.118975	+	0.159811i
$195$		0			0
$196$	9.95831	−	6.54968i	0.711308	−	0.467834i
$197$	−21.2308	−	7.72738i	−1.51263	−	0.550553i	−0.553336	−	0.832958i	$-0.686646\pi$
$197$	−21.2308	−	7.72738i	−1.51263	−	0.550553i	−0.959295	+	0.282405i	$0.908868\pi$
$198$		0			0
$199$	−13.8558	+	5.04311i	−0.982214	+	0.357497i	−0.782700	−	0.622399i	$-0.786158\pi$
$199$	−13.8558	+	5.04311i	−0.982214	+	0.357497i	−0.199513	+	0.979895i	$0.563936\pi$
$200$	−1.36374	+	1.83182i	−0.0964312	+	0.129530i
$201$		0			0
$202$	0.0310297	−	0.0328896i	0.00218324	−	0.00231410i
$203$	−5.13101	+	5.43855i	−0.360126	+	0.381712i
$204$		0			0
$205$	−9.91643	+	13.3201i	−0.692593	+	0.930314i
$206$	3.91682	−	1.42561i	0.272898	−	0.0993267i
$207$		0			0
$208$	−11.9249	−	4.34031i	−0.826844	−	0.300947i
$209$	−3.75902	+	2.47234i	−0.260017	+	0.171016i
$210$		0			0
$211$	−7.75451	−	10.4161i	−0.533843	−	0.717075i	0.450611	−	0.892720i	$-0.351206\pi$
$211$	−7.75451	−	10.4161i	−0.533843	−	0.717075i	−0.984453	+	0.175645i	$0.943799\pi$
$212$	21.0447	+	13.8413i	1.44536	+	0.950625i
$213$		0			0
$214$	0.0743122	−	0.248220i	0.00507988	−	0.0169680i
$215$	−13.2703	+	22.9849i	−0.905028	+	1.56755i
$216$		0			0
$217$	−2.38058	−	4.12329i	−0.161604	−	0.279907i
$218$	1.44095	−	0.341511i	0.0975934	−	0.0231301i
$219$		0			0
$220$	−11.2352	+	5.64253i	−0.757477	+	0.380419i
$221$	2.85258	−	6.61303i	0.191885	−	0.444840i
$222$		0			0
$223$	0.862925	+	14.8159i	0.0577858	+	0.992143i	0.895226	+	0.445613i	$0.147014\pi$
$223$	0.862925	+	14.8159i	0.0577858	+	0.992143i	−0.837440	+	0.546530i	$0.815949\pi$
$224$	2.17478	+	12.3338i	0.145309	+	0.824086i
$225$		0			0
$226$	−0.485421	+	2.75296i	−0.0322897	+	0.183124i
$227$	−5.56455	−	0.650403i	−0.369332	−	0.0431687i	−0.0705973	−	0.997505i	$-0.522491\pi$
$227$	−5.56455	−	0.650403i	−0.369332	−	0.0431687i	−0.298735	+	0.954336i	$0.596565\pi$
$228$		0			0
$229$	5.71315	+	19.0833i	0.377536	+	1.26106i	0.910001	+	0.414605i	$0.136080\pi$
$229$	5.71315	+	19.0833i	0.377536	+	1.26106i	−0.532466	+	0.846452i	$0.678734\pi$
$230$	6.64112	+	1.57398i	0.437903	+	0.103785i
$231$		0			0
$232$	−0.970920	−	2.25084i	−0.0637440	−	0.147775i
$233$	4.48492	+	3.76330i	0.293817	+	0.246542i	0.777765	−	0.628555i	$-0.216353\pi$
$233$	4.48492	+	3.76330i	0.293817	+	0.246542i	−0.483948	+	0.875097i	$0.660798\pi$
$234$		0			0
$235$	−18.5899	+	15.5988i	−1.21267	+	1.01755i
$236$	−1.59303	−	0.800048i	−0.103697	−	0.0520787i
$237$		0			0
$238$	−2.16186	+	0.252686i	−0.140133	+	0.0163792i
$239$	0.867269	−	14.8904i	0.0560990	−	0.963182i	−0.846416	−	0.532523i	$-0.821244\pi$
$239$	0.867269	−	14.8904i	0.0560990	−	0.963182i	0.902515	−	0.430659i	$-0.141719\pi$
$240$		0			0
$241$	0.154366	+	0.163618i	0.00994358	+	0.0105396i	0.732326	−	0.680954i	$-0.238435\pi$
$241$	0.154366	+	0.163618i	0.00994358	+	0.0105396i	−0.722383	+	0.691493i	$0.756953\pi$
$242$	−1.43913			−0.0925107
$243$		0			0
$244$	3.76497			0.241027
$245$	−11.2797	−	11.9557i	−0.720631	−	0.763824i
$246$		0			0
$247$	−0.383846	+	6.59037i	−0.0244235	+	0.419335i
$248$	1.55039	−	0.181215i	0.0984500	−	0.0115072i
$249$		0			0
$250$	−2.21547	−	1.11265i	−0.140118	−	0.0703701i
$251$	−0.0887945	+	0.0745074i	−0.00560466	+	0.00470286i	−0.645586	−	0.763688i	$-0.723387\pi$
$251$	−0.0887945	+	0.0745074i	−0.00560466	+	0.00470286i	0.639981	+	0.768391i	$0.278942\pi$
$252$		0			0
$253$	16.3234	+	13.6970i	1.02624	+	0.861120i
$254$	0.0929519	+	0.215487i	0.00583232	+	0.0135208i
$255$		0			0
$256$	8.80153	+	2.08600i	0.550096	+	0.130375i
$257$	2.56548	+	8.56931i	0.160030	+	0.534539i	0.999967	−	0.00814612i	$-0.00259302\pi$
$257$	2.56548	+	8.56931i	0.160030	+	0.534539i	−0.839936	+	0.542685i	$0.817408\pi$
$258$		0			0
$259$	19.1764	+	2.24140i	1.19156	+	0.139274i
$260$	−3.20334	+	18.1671i	−0.198663	+	1.12667i
$261$		0			0
$262$	−0.429681	−	2.43684i	−0.0265458	−	0.150549i
$263$	−0.918483	−	15.7697i	−0.0566361	−	0.972404i	−0.900228	−	0.435419i	$-0.856600\pi$
$263$	−0.918483	−	15.7697i	−0.0566361	−	0.972404i	0.843592	−	0.536985i	$-0.180437\pi$
$264$		0			0
$265$	13.7581	−	31.8949i	0.845154	−	1.95929i
$266$	1.78289	−	0.895400i	0.109316	−	0.0549005i
$267$		0			0
$268$	−11.0788	+	2.62572i	−0.676744	+	0.160391i
$269$	−12.1223	−	20.9965i	−0.739111	−	1.28018i	−0.952896	−	0.303298i	$-0.901912\pi$
$269$	−12.1223	−	20.9965i	−0.739111	−	1.28018i	0.213784	−	0.976881i	$-0.431421\pi$
$270$		0			0
$271$	7.20041	−	12.4715i	0.437394	−	0.757588i	−0.560094	−	0.828429i	$-0.689235\pi$
$271$	7.20041	−	12.4715i	0.437394	−	0.757588i	0.997488	+	0.0708408i	$0.0225682\pi$
$272$	−1.93597	+	6.46657i	−0.117385	+	0.392094i
$273$		0			0
$274$	2.35550	+	1.54924i	0.142301	+	0.0935928i
$275$	2.86565	+	3.84924i	0.172805	+	0.232118i
$276$		0			0
$277$	23.2263	−	15.2762i	1.39553	−	0.917858i	0.395535	−	0.918451i	$-0.370559\pi$
$277$	23.2263	−	15.2762i	1.39553	−	0.917858i	1.00000		0.000593349i	$0.000188869\pi$
$278$	2.87024	+	1.04468i	0.172145	+	0.0626558i
$279$		0			0
$280$	10.7342	−	3.90692i	0.641490	−	0.233483i
$281$	−6.08566	+	8.17446i	−0.363040	+	0.487648i	−0.945687	−	0.325078i	$-0.894610\pi$
$281$	−6.08566	+	8.17446i	−0.363040	+	0.487648i	0.582647	+	0.812725i	$0.302017\pi$
$282$		0			0
$283$	−19.8426	+	21.0320i	−1.17952	+	1.25022i	−0.217860	+	0.975980i	$0.569908\pi$
$283$	−19.8426	+	21.0320i	−1.17952	+	1.25022i	−0.961661	+	0.274240i	$0.911574\pi$
$284$	−8.50123	+	9.01078i	−0.504455	+	0.534692i
$285$		0			0
$286$	1.68339	−	2.26119i	0.0995412	−	0.133707i
$287$	21.6038	−	7.86313i	1.27523	−	0.464146i
$288$		0			0
$289$	12.3749	+	4.50410i	0.727936	+	0.264947i
$290$	−1.37843	+	0.906606i	−0.0809440	+	0.0532377i
$291$		0			0
$292$	7.50411	+	10.0798i	0.439145	+	0.589874i
$293$	−24.7672	−	16.2897i	−1.44692	−	0.951653i	−0.998321	−	0.0579180i	$-0.981554\pi$
$293$	−24.7672	−	16.2897i	−1.44692	−	0.951653i	−0.448596	−	0.893735i	$-0.648076\pi$
$294$		0			0
$295$	−0.705053	+	2.35504i	−0.0410498	+	0.137116i
$296$	−3.16489	+	5.48175i	−0.183955	+	0.318620i
$297$		0			0
$298$	−0.251082	−	0.434887i	−0.0145448	−	0.0251923i
$299$	30.4229	−	7.21036i	1.75940	−	0.416986i
$300$		0			0
$301$	32.8359	−	16.4908i	1.89263	−	0.950514i
$302$	−1.80493	+	4.18430i	−0.103862	+	0.240779i
$303$		0			0
$304$	−0.359762	−	6.17687i	−0.0206337	−	0.354268i
$305$	−0.901581	−	5.11312i	−0.0516244	−	0.292776i
$306$		0			0
$307$	1.79762	−	10.1948i	0.102595	−	0.581848i	−0.889558	−	0.456822i	$-0.848988\pi$
$307$	1.79762	−	10.1948i	0.102595	−	0.581848i	0.992154	−	0.125026i	$-0.0399013\pi$
$308$	17.2884	+	2.02072i	0.985095	+	0.115141i
$309$		0			0
$310$	−0.301311	−	1.00645i	−0.0171133	−	0.0571625i
$311$	−7.82499	−	1.85456i	−0.443715	−	0.105162i	0.00268428	−	0.999996i	$-0.499146\pi$
$311$	−7.82499	−	1.85456i	−0.443715	−	0.105162i	−0.446399	+	0.894834i	$0.647294\pi$
$312$		0			0
$313$	1.33728	+	3.10017i	0.0755878	+	0.175232i	0.951820	−	0.306656i	$-0.0992103\pi$
$313$	1.33728	+	3.10017i	0.0755878	+	0.175232i	−0.876232	+	0.481889i	$0.839951\pi$
$314$	−0.0634701	−	0.0532577i	−0.00358182	−	0.00300551i
$315$		0			0
$316$	16.9819	−	14.2495i	0.955306	−	0.801597i
$317$	9.93585	+	4.98997i	0.558053	+	0.280265i	0.705387	−	0.708822i	$-0.250773\pi$
$317$	9.93585	+	4.98997i	0.558053	+	0.280265i	−0.147335	+	0.989087i	$0.547069\pi$
$318$		0			0
$319$	−5.11617	+	0.597994i	−0.286451	+	0.0334813i
$320$	0.893837	−	15.3466i	0.0499670	−	0.857900i
$321$		0			0
$322$	−6.48432	−	6.87297i	−0.361357	−	0.383016i
$323$	3.51148			0.195384
$324$		0			0
$325$	7.04117			0.390574
$326$	0.409428	+	0.433969i	0.0226761	+	0.0240353i
$327$		0			0
$328$	−0.438258	+	7.52460i	−0.0241987	+	0.415476i
$329$	33.3699	−	3.90038i	1.83974	−	0.215035i
$330$		0			0
$331$	−18.9468	−	9.51544i	−1.04141	−	0.523016i	−0.155966	−	0.987762i	$-0.549849\pi$
$331$	−18.9468	−	9.51544i	−1.04141	−	0.523016i	−0.885444	+	0.464746i	$0.846145\pi$
$332$	24.9136	−	20.9050i	1.36731	−	1.14731i
$333$		0			0
$334$	1.79297	+	1.50448i	0.0981071	+	0.0823216i
$335$	6.21892	+	14.4171i	0.339776	+	0.787689i
$336$		0			0
$337$	−12.8257	−	3.03974i	−0.698658	−	0.165585i	−0.134087	−	0.990970i	$-0.542810\pi$
$337$	−12.8257	−	3.03974i	−0.698658	−	0.165585i	−0.564571	+	0.825384i	$0.690958\pi$
$338$	−0.0472916	−	0.157965i	−0.00257233	−	0.00859217i
$339$		0			0
$340$	9.74609	+	1.13916i	0.528556	+	0.0617794i
$341$	0.569573	−	3.23021i	0.0308441	−	0.174926i
$342$		0			0
$343$	−0.473286	−	2.68414i	−0.0255550	−	0.144930i
$344$	0.700447	+	12.0262i	0.0377656	+	0.648410i
$345$		0			0
$346$	0.732986	−	1.69925i	0.0394056	−	0.0913524i
$347$	10.3023	−	5.17399i	0.553055	−	0.277754i	−0.150244	−	0.988649i	$-0.548006\pi$
$347$	10.3023	−	5.17399i	0.553055	−	0.277754i	0.703299	+	0.710895i	$0.251710\pi$
$348$		0			0
$349$	7.74090	−	1.83463i	0.414361	−	0.0982053i	−0.0181475	−	0.999835i	$-0.505777\pi$
$349$	7.74090	−	1.83463i	0.414361	−	0.0982053i	0.432508	+	0.901630i	$0.357629\pi$
$350$	−1.06398	−	1.84287i	−0.0568722	−	0.0985056i
$351$		0			0
$352$	−4.31401	+	7.47208i	−0.229937	+	0.398263i
$353$	−0.766919	+	2.56169i	−0.0408190	+	0.136345i	−0.975970	−	0.217904i	$-0.930078\pi$
$353$	−0.766919	+	2.56169i	−0.0408190	+	0.136345i	0.935151	+	0.354249i	$0.115263\pi$
$354$		0			0
$355$	14.2731	+	9.38757i	0.757538	+	0.498241i
$356$	−5.42145	−	7.28228i	−0.287336	−	0.385960i
$357$		0			0
$358$	0.705360	−	0.463922i	0.0372794	−	0.0245191i
$359$	−18.3022	−	6.66145i	−0.965952	−	0.351578i	−0.189589	−	0.981864i	$-0.560715\pi$
$359$	−18.3022	−	6.66145i	−0.965952	−	0.351578i	−0.776363	+	0.630286i	$0.782938\pi$
$360$		0			0
$361$	14.8296	−	5.39752i	0.780504	−	0.284080i
$362$	1.60839	−	2.16045i	0.0845353	−	0.113551i
$363$		0			0
$364$	17.5262	−	18.5767i	0.918624	−	0.973684i
$365$	11.8921	−	12.6049i	0.622463	−	0.659772i
$366$		0			0
$367$	−6.29899	+	8.46101i	−0.328805	+	0.441661i	−0.935528	−	0.353251i	$-0.885076\pi$
$367$	−6.29899	+	8.46101i	−0.328805	+	0.441661i	0.606724	+	0.794913i	$0.292483\pi$
$368$	−27.5367	+	10.0225i	−1.43545	+	0.522461i
$369$		0			0
$370$	4.00329	+	1.45708i	0.208121	+	0.0757499i
$371$	−40.1786	+	26.4259i	−2.08597	+	1.37196i
$372$		0			0
$373$	−11.2482	−	15.1089i	−0.582409	−	0.782311i	0.409081	−	0.912498i	$-0.365849\pi$
$373$	−11.2482	−	15.1089i	−0.582409	−	0.782311i	−0.991489	+	0.130188i	$0.958442\pi$
$374$	−1.25280	−	0.823977i	−0.0647806	−	0.0426068i
$375$		0			0
$376$	−3.15908	+	10.5521i	−0.162917	+	0.544181i
$377$	−3.77896	+	6.54536i	−0.194626	+	0.337103i
$378$		0			0
$379$	4.33052	+	7.50069i	0.222444	+	0.385285i	0.955550	−	0.294830i	$-0.0952632\pi$
$379$	4.33052	+	7.50069i	0.222444	+	0.385285i	−0.733105	+	0.680115i	$0.761930\pi$
$380$	−8.75186	+	2.07423i	−0.448961	+	0.106406i
$381$		0			0
$382$	−0.505700	+	0.253972i	−0.0258739	+	0.0129943i
$383$	11.9841	−	27.7823i	0.612360	−	1.41961i	−0.276313	−	0.961068i	$-0.589113\pi$
$383$	11.9841	−	27.7823i	0.612360	−	1.41961i	0.888673	−	0.458542i	$-0.151628\pi$
$384$		0			0
$385$	−1.39568	−	23.9628i	−0.0711303	−	1.22126i
$386$	0.0183406	+	0.104015i	0.000933511	+	0.00529420i
$387$		0			0
$388$	−3.00757	+	17.0568i	−0.152686	+	0.865928i
$389$	16.1739	+	1.89045i	0.820047	+	0.0958498i	0.515763	−	0.856731i	$-0.327509\pi$
$389$	16.1739	+	1.89045i	0.820047	+	0.0958498i	0.304285	+	0.952581i	$0.401583\pi$
$390$		0			0
$391$	−4.76975	−	15.9321i	−0.241217	−	0.805720i
$392$	−7.25947	−	1.72053i	−0.366659	−	0.0868997i
$393$		0			0
$394$	2.73375	+	6.33755i	0.137724	+	0.319281i
$395$	−23.4185	−	19.6505i	−1.17831	−	0.988723i
$396$		0			0
$397$	22.8963	−	19.2123i	1.14913	−	0.964236i	0.149433	−	0.988772i	$-0.452255\pi$
$397$	22.8963	−	19.2123i	1.14913	−	0.964236i	0.999699	+	0.0245358i	$0.00781077\pi$
$398$	4.02533	+	2.02160i	0.201772	+	0.101334i
$399$		0			0
$400$	−6.55476	+	0.766141i	−0.327738	+	0.0383071i
$401$	−1.81797	+	31.2134i	−0.0907852	+	1.55872i	0.578479	+	0.815697i	$0.303646\pi$
$401$	−1.81797	+	31.2134i	−0.0907852	+	1.55872i	−0.669264	+	0.743024i	$0.733391\pi$
$402$		0			0
$403$	−3.30268	−	3.50064i	−0.164518	−	0.174379i
$404$	0.282216			0.0140408
$405$		0			0
$406$	2.28414			0.113360
$407$	9.12759	+	9.67468i	0.452438	+	0.479556i
$408$		0			0
$409$	1.53256	−	26.3131i	0.0757803	−	1.30110i	−0.719345	−	0.694653i	$-0.755558\pi$
$409$	1.53256	−	26.3131i	0.0757803	−	1.30110i	0.795125	−	0.606445i	$-0.207405\pi$
$410$	5.03866	−	0.588935i	0.248842	−	0.0290854i
$411$		0			0
$412$	23.2481	+	11.6756i	1.14535	+	0.575218i
$413$	2.60717	−	2.18768i	0.128291	−	0.107649i
$414$		0			0
$415$	−34.3566	−	28.8286i	−1.68650	−	1.41514i
$416$	5.01423	+	11.6243i	0.245843	+	0.569928i
$417$		0			0
$418$	1.33741	+	0.316971i	0.0654147	+	0.0155036i
$419$	4.50019	+	15.0317i	0.219849	+	0.734346i	0.994757	+	0.102272i	$0.0326111\pi$
$419$	4.50019	+	15.0317i	0.219849	+	0.734346i	−0.774908	+	0.632074i	$0.782204\pi$
$420$		0			0
$421$	22.6407	+	2.64632i	1.10344	+	0.128974i	0.648255	−	0.761423i	$-0.275499\pi$
$421$	22.6407	+	2.64632i	1.10344	+	0.128974i	0.455185	+	0.890397i	$0.349573\pi$
$422$	−0.688860	+	3.90672i	−0.0335332	+	0.190176i
$423$		0			0
$424$	−2.73779	−	15.5268i	−0.132959	−	0.754046i
$425$	−0.217771	−	3.73898i	−0.0105634	−	0.181367i
$426$		0			0
$427$	−2.84705	+	6.60021i	−0.137779	+	0.319407i
$428$	1.44516	−	0.725786i	0.0698544	−	0.0350822i
$429$		0			0
$430$	7.88933	−	1.86981i	0.380457	−	0.0901701i
$431$	−17.0699	−	29.5659i	−0.822227	−	1.42414i	−0.904020	−	0.427490i	$-0.859398\pi$
$431$	−17.0699	−	29.5659i	−0.822227	−	1.42414i	0.0817934	−	0.996649i	$-0.473935\pi$
$432$		0			0
$433$	−11.6224	+	20.1306i	−0.558539	+	0.967417i	0.439080	+	0.898448i	$0.355304\pi$
$433$	−11.6224	+	20.1306i	−0.558539	+	0.967417i	−0.997619	+	0.0689692i	$0.978029\pi$
$434$	−0.417151	+	1.39338i	−0.0200239	+	0.0668845i
$435$		0			0
$436$	7.72213	+	5.07892i	0.369823	+	0.243236i
$437$	9.10315	+	12.2277i	0.435463	+	0.584928i
$438$		0			0
$439$	−5.76713	+	3.79310i	−0.275250	+	0.181035i	−0.679627	−	0.733557i	$-0.737859\pi$
$439$	−5.76713	+	3.79310i	−0.275250	+	0.181035i	0.404378	+	0.914592i	$0.367488\pi$
$440$	7.39493	+	2.69154i	0.352540	+	0.128314i
$441$		0			0
$442$	−2.06746	+	0.752494i	−0.0983391	+	0.0357925i
$443$	−9.62688	+	12.9311i	−0.457387	+	0.614377i	−0.969664	−	0.244443i	$-0.921395\pi$
$443$	−9.62688	+	12.9311i	−0.457387	+	0.614377i	0.512277	+	0.858821i	$0.328802\pi$
$444$		0			0
$445$	−8.59165	+	9.10662i	−0.407283	+	0.431695i
$446$	3.11125	−	3.29774i	0.147322	−	0.156152i
$447$		0			0
$448$	−12.7091	+	17.0713i	−0.600449	+	0.806543i
$449$	−20.7990	+	7.57021i	−0.981565	+	0.357261i	−0.782449	−	0.622715i	$-0.786029\pi$
$449$	−20.7990	+	7.57021i	−0.981565	+	0.357261i	−0.199117	+	0.979976i	$0.563807\pi$
$450$		0			0
$451$	14.8832	+	5.41703i	0.700821	+	0.255078i
$452$	−14.5770	+	9.58746i	−0.685646	+	0.450956i
$453$		0			0
$454$	1.02203	+	1.37282i	0.0479661	+	0.0644297i
$455$	−29.4256	−	19.3535i	−1.37949	−	0.907306i
$456$		0			0
$457$	7.44649	−	24.8730i	0.348332	−	1.16351i	−0.586954	−	0.809620i	$-0.699673\pi$
$457$	7.44649	−	24.8730i	0.348332	−	1.16351i	0.935287	−	0.353891i	$-0.115142\pi$
$458$	3.04269	−	5.27010i	0.142176	−	0.246255i
$459$		0			0
$460$	21.2990	+	36.8910i	0.993072	+	1.72005i
$461$	2.21895	−	0.525901i	0.103347	−	0.0244936i	−0.178617	−	0.983919i	$-0.557162\pi$
$461$	2.21895	−	0.525901i	0.103347	−	0.0244936i	0.281964	+	0.959425i	$0.409014\pi$
$462$		0			0
$463$	4.93891	−	2.48041i	0.229530	−	0.115275i	−0.330318	−	0.943870i	$-0.607156\pi$
$463$	4.93891	−	2.48041i	0.229530	−	0.115275i	0.559848	+	0.828595i	$0.310860\pi$
$464$	2.80571	−	6.50438i	0.130252	−	0.301958i
$465$		0			0
$466$	−0.103994	−	1.78551i	−0.00481743	−	0.0827120i
$467$	4.62726	+	26.2425i	0.214124	+	1.21436i	0.882420	+	0.470463i	$0.155913\pi$
$467$	4.62726	+	26.2425i	0.214124	+	1.21436i	−0.668296	+	0.743896i	$0.732976\pi$
$468$		0			0
$469$	3.77469	−	21.4073i	0.174299	−	0.988498i
$470$	7.36331	+	0.860647i	0.339644	+	0.0396987i
$471$		0			0
$472$	0.320018	+	1.06894i	0.0147300	+	0.0492018i
$473$	24.6313	+	5.83774i	1.13255	+	0.268419i
$474$		0			0
$475$	1.35976	+	3.15227i	0.0623900	+	0.144636i
$476$	−10.4066	−	8.73219i	−0.476986	−	0.400239i
$477$		0			0
$478$	−3.49054	+	2.92891i	−0.159654	+	0.133965i
$479$	−17.2897	−	8.68320i	−0.789985	−	0.396745i	0.00758547	−	0.999971i	$-0.497585\pi$
$479$	−17.2897	−	8.68320i	−0.789985	−	0.396745i	−0.797570	+	0.603226i	$0.793882\pi$
$480$		0			0
$481$	19.3840	−	2.26567i	0.883835	−	0.103306i
$482$	0.00399560	−	0.0686017i	0.000181994	−	0.00312472i
$483$		0			0
$484$	−6.16393	−	6.53338i	−0.280178	−	0.296972i
$485$	23.8847			1.08455
$486$		0			0
$487$	−23.9390			−1.08478			−0.542390	−	0.840127i	$-0.682480\pi$
$487$	−23.9390			−1.08478			−0.542390	+	0.840127i	$0.682480\pi$
$488$	−1.61720	−	1.71414i	−0.0732074	−	0.0775953i
$489$		0			0
$490$	−0.291962	+	5.01279i	−0.0131895	+	0.226455i
$491$	−27.1437	+	3.17264i	−1.22498	+	0.143179i	−0.703880	−	0.710319i	$-0.748551\pi$
$491$	−27.1437	+	3.17264i	−1.22498	+	0.143179i	−0.521096	+	0.853498i	$0.674477\pi$
$492$		0			0
$493$	3.59257	+	1.80426i	0.161801	+	0.0812597i
$494$	1.54488	−	1.29631i	0.0695076	−	0.0583238i
$495$		0			0
$496$	3.45543	+	2.89945i	0.155153	+	0.130189i
$497$	−9.36784	−	21.7171i	−0.420205	−	0.974145i
$498$		0			0
$499$	−9.28432	−	2.20042i	−0.415623	−	0.0985045i	0.0174836	−	0.999847i	$-0.494435\pi$
$499$	−9.28432	−	2.20042i	−0.415623	−	0.0985045i	−0.433107	+	0.901343i	$0.642583\pi$
$500$	−4.43783	−	14.8234i	−0.198466	−	0.662923i
$501$		0			0
$502$	0.0351707	+	0.00411087i	0.00156975	+	0.000183477i
$503$	−6.80145	+	38.5730i	−0.303262	+	1.71988i	0.328314	+	0.944569i	$0.393520\pi$
$503$	−6.80145	+	38.5730i	−0.303262	+	1.71988i	−0.631575	+	0.775314i	$0.717591\pi$
$504$		0			0
$505$	−0.0675811	−	0.383272i	−0.00300732	−	0.0170554i
$506$	−0.378498	−	6.49856i	−0.0168263	−	0.288896i
$507$		0			0
$508$	−0.580149	+	1.34494i	−0.0257399	+	0.0596719i
$509$	−0.950909	+	0.477564i	−0.0421483	+	0.0211677i	−0.469749	−	0.882800i	$-0.655655\pi$
$509$	−0.950909	+	0.477564i	−0.0421483	+	0.0211677i	0.427600	+	0.903968i	$0.359359\pi$
$510$		0			0
$511$	−23.3450	+	5.53287i	−1.03272	+	0.244760i
$512$	−10.0486	−	17.4047i	−0.444089	−	0.769185i
$513$		0			0
$514$	1.36632	−	2.36653i	0.0602656	−	0.104383i
$515$	10.2893	−	34.3687i	0.453401	−	1.51447i
$516$		0			0
$517$	19.3378	+	12.7187i	0.850476	+	0.559367i
$518$	−3.52208	−	4.73098i	−0.154751	−	0.207867i
$519$		0			0
$520$	9.64717	−	6.34504i	0.423056	−	0.278248i
$521$	42.0204	+	15.2942i	1.84095	+	0.670050i	0.989293	+	0.145946i	$0.0466226\pi$
$521$	42.0204	+	15.2942i	1.84095	+	0.670050i	0.851654	+	0.524104i	$0.175600\pi$
$522$		0			0
$523$	−27.5645	+	10.0326i	−1.20531	+	0.438697i	−0.865075	−	0.501643i	$-0.832729\pi$
$523$	−27.5645	+	10.0326i	−1.20531	+	0.438697i	−0.340236	+	0.940340i	$0.610507\pi$
$524$	9.22245	−	12.3879i	0.402885	−	0.541168i
$525$		0			0
$526$	−3.31156	+	3.51005i	−0.144391	+	0.153046i
$527$	−1.75676	+	1.86205i	−0.0765255	+	0.0811123i
$528$		0			0
$529$	29.3789	−	39.4627i	1.27734	−	1.71577i
$530$	−9.97144	+	3.62931i	−0.433132	+	0.157647i
$531$		0			0
$532$	11.7012	+	4.25890i	0.507313	+	0.184647i
$533$	19.4160	−	12.7701i	0.841002	−	0.553136i
$534$		0			0
$535$	−1.33174	−	1.78884i	−0.0575762	−	0.0773383i
$536$	5.95423	+	3.91616i	0.257184	+	0.169152i
$537$		0			0
$538$	−2.12420	+	7.09534i	−0.0915810	+	0.305902i
$539$	−7.83850	+	13.5767i	−0.337628	+	0.584789i
$540$		0			0
$541$	−14.0760	−	24.3804i	−0.605176	−	1.04820i	−0.992024	−	0.126052i	$-0.959769\pi$
$541$	−14.0760	−	24.3804i	−0.605176	−	1.04820i	0.386848	−	0.922144i	$-0.373564\pi$
$542$	−4.28072	+	1.01455i	−0.183873	+	0.0435786i
$543$		0			0
$544$	6.01762	−	3.02216i	0.258004	−	0.129574i
$545$	5.04839	−	11.7035i	0.216249	−	0.501322i
$546$		0			0
$547$	−0.295527	−	5.07399i	−0.0126358	−	0.216948i	−0.998715	−	0.0506736i	$-0.983863\pi$
$547$	−0.295527	−	5.07399i	−0.0126358	−	0.216948i	0.986079	−	0.166275i	$-0.0531739\pi$
$548$	3.05558	+	17.3291i	0.130528	+	0.740261i
$549$		0			0
$550$	0.254566	−	1.44371i	0.0108547	−	0.0615602i
$551$	−3.66008	−	0.427802i	−0.155925	−	0.0182250i
$552$		0			0
$553$	12.1386	+	40.5457i	0.516185	+	1.72418i
$554$	−8.26360	−	1.95851i	−0.351087	−	0.0832091i
$555$		0			0
$556$	7.55084	+	17.5048i	0.320227	+	0.742369i
$557$	15.3731	+	12.8995i	0.651378	+	0.546571i	0.907489	−	0.420076i	$-0.137997\pi$
$557$	15.3731	+	12.8995i	0.651378	+	0.546571i	−0.256111	+	0.966647i	$0.582441\pi$
$558$		0			0
$559$	28.4525	−	23.8745i	1.20341	−	1.00978i
$560$	29.4986	+	14.8148i	1.24655	+	0.626039i
$561$		0			0
$562$	3.09220	−	0.361427i	0.130437	−	0.0152459i
$563$	−2.00185	+	34.3704i	−0.0843677	+	1.44854i	0.644878	+	0.764286i	$0.276908\pi$
$563$	−2.00185	+	34.3704i	−0.0843677	+	1.44854i	−0.729246	+	0.684252i	$0.760129\pi$
$564$		0			0
$565$	16.5112	+	17.5009i	0.694633	+	0.736267i
$566$	8.83320			0.371287
$567$		0			0
$568$	7.75410			0.325355
$569$	−9.36443	−	9.92572i	−0.392577	−	0.416108i	0.500695	−	0.865624i	$-0.333078\pi$
$569$	−9.36443	−	9.92572i	−0.392577	−	0.416108i	−0.893272	+	0.449516i	$0.851596\pi$
$570$		0			0
$571$	−1.27488	+	21.8888i	−0.0533519	+	0.916016i	0.860368	+	0.509673i	$0.170233\pi$
$571$	−1.27488	+	21.8888i	−0.0533519	+	0.916016i	−0.913720	+	0.406344i	$0.866804\pi$
$572$	17.4755	−	2.04260i	0.730689	−	0.0854053i
$573$		0			0
$574$	−6.27623	−	3.15204i	−0.261965	−	0.131564i
$575$	12.4553	−	10.4513i	0.519423	−	0.435848i
$576$		0			0
$577$	−4.05986	−	3.40663i	−0.169014	−	0.141820i	0.554357	−	0.832279i	$-0.312964\pi$
$577$	−4.05986	−	3.40663i	−0.169014	−	0.141820i	−0.723371	+	0.690459i	$0.757409\pi$
$578$	−1.59344	−	3.69401i	−0.0662783	−	0.153650i
$579$		0			0
$580$	−10.0198	−	2.37473i	−0.416048	−	0.0986052i
$581$	17.8081	+	59.4833i	0.738805	+	2.46778i
$582$		0			0
$583$	−32.9059	−	3.84615i	−1.36282	−	0.159291i
$584$	1.36586	−	7.74618i	0.0565197	−	0.320539i
$585$		0			0
$586$	1.57255	+	8.91836i	0.0649614	+	0.368414i
$587$	−0.257492	−	4.42097i	−0.0106278	−	0.182473i	−0.999444	−	0.0333349i	$-0.989387\pi$
$587$	−0.257492	−	4.42097i	−0.0106278	−	0.182473i	0.988816	−	0.149138i	$-0.0476498\pi$
$588$		0			0
$589$	0.929409	−	2.15461i	0.0382956	−	0.0887793i
$590$	0.671109	−	0.337044i	0.0276291	−	0.0138759i
$591$		0			0
$592$	−17.7984	+	4.21830i	−0.731511	+	0.173371i
$593$	−1.66347	−	2.88121i	−0.0683104	−	0.118317i	0.829847	−	0.557991i	$-0.188428\pi$
$593$	−1.66347	−	2.88121i	−0.0683104	−	0.118317i	−0.898158	+	0.439673i	$0.855094\pi$
$594$		0			0
$595$	−9.36697	+	16.2241i	−0.384008	+	0.665122i
$596$	0.898899	−	3.00253i	0.0368203	−	0.122988i
$597$		0			0
$598$	−7.98002	−	5.24854i	−0.326327	−	0.214629i
$599$	6.36334	+	8.54745i	0.259999	+	0.349239i	0.912885	−	0.408217i	$-0.133849\pi$
$599$	6.36334	+	8.54745i	0.259999	+	0.349239i	−0.652886	+	0.757456i	$0.726442\pi$
$600$		0			0
$601$	−4.74246	+	3.11917i	−0.193449	+	0.127233i	−0.642539	−	0.766253i	$-0.722119\pi$
$601$	−4.74246	+	3.11917i	−0.193449	+	0.127233i	0.449090	+	0.893487i	$0.351748\pi$
$602$	−10.5480	−	3.83917i	−0.429906	−	0.156473i
$603$		0			0
$604$	−26.7266	+	9.72770i	−1.08749	+	0.395814i
$605$	−7.39680	+	9.93562i	−0.300722	+	0.403940i
$606$		0			0
$607$	2.11017	−	2.23665i	0.0856490	−	0.0907827i	−0.683131	−	0.730295i	$-0.739382\pi$
$607$	2.11017	−	2.23665i	0.0856490	−	0.0907827i	0.768780	+	0.639513i	$0.220864\pi$
$608$	−4.23578	+	4.48966i	−0.171784	+	0.182080i
$609$		0			0
$610$	−0.947154	+	1.27225i	−0.0383491	+	0.0515118i
$611$	31.9127	−	11.6153i	1.29105	−	0.469904i
$612$		0			0
$613$	−14.0676	−	5.12017i	−0.568184	−	0.206802i	0.0419236	−	0.999121i	$-0.486651\pi$
$613$	−14.0676	−	5.12017i	−0.568184	−	0.206802i	−0.610107	+	0.792319i	$0.708874\pi$
$614$	−2.64219	+	1.73779i	−0.106630	+	0.0701316i
$615$		0			0
$616$	−6.50604	−	8.73912i	−0.262136	−	0.352109i
$617$	−17.9829	−	11.8275i	−0.723963	−	0.476158i	0.133275	−	0.991079i	$-0.457451\pi$
$617$	−17.9829	−	11.8275i	−0.723963	−	0.476158i	−0.857237	+	0.514921i	$0.827821\pi$
$618$		0			0
$619$	−12.0899	+	40.3832i	−0.485936	+	1.62314i	0.266050	+	0.963959i	$0.414281\pi$
$619$	−12.0899	+	40.3832i	−0.485936	+	1.62314i	−0.751986	+	0.659179i	$0.770904\pi$
$620$	3.27855	−	5.67862i	0.131670	−	0.228059i
$621$		0			0
$622$	1.22834	+	2.12754i	0.0492518	+	0.0853066i
$623$	16.8659	−	3.99730i	0.675720	−	0.160149i
$624$		0			0
$625$	−27.6187	+	13.8706i	−1.10475	+	0.554825i
$626$	0.408526	−	0.947070i	0.0163280	−	0.0378525i
$627$		0			0
$628$	−0.0300682	−	0.516250i	−0.00119985	−	0.0206006i
$629$	−1.80262	−	10.2232i	−0.0718753	−	0.407625i
$630$		0			0
$631$	−0.662591	+	3.75774i	−0.0263773	+	0.149593i	−0.995152	−	0.0983500i	$-0.968644\pi$
$631$	−0.662591	+	3.75774i	−0.0263773	+	0.149593i	0.968775	+	0.247943i	$0.0797547\pi$
$632$	−13.7820	−	1.61089i	−0.548219	−	0.0640776i
$633$		0			0
$634$	−0.974150	−	3.25389i	−0.0386885	−	0.129228i
$635$	1.96545	+	0.465821i	0.0779967	+	0.0184856i
$636$		0			0
$637$	9.11080	+	21.1212i	0.360983	+	0.836853i
$638$	1.20543	+	1.01148i	0.0477234	+	0.0400447i
$639$		0			0
$640$	−17.4571	+	14.6482i	−0.690051	+	0.579022i
$641$	−41.6396	−	20.9122i	−1.64467	−	0.825983i	−0.998000	−	0.0632098i	$-0.979866\pi$
$641$	−41.6396	−	20.9122i	−1.64467	−	0.825983i	−0.646666	−	0.762773i	$-0.723837\pi$
$642$		0			0
$643$	−7.06749	+	0.826071i	−0.278714	+	0.0325770i	−0.254302	−	0.967125i	$-0.581846\pi$
$643$	−7.06749	+	0.826071i	−0.278714	+	0.0325770i	−0.0244127	+	0.999702i	$0.507772\pi$
$644$	3.42909	−	58.8752i	0.135125	−	2.32001i
$645$		0			0
$646$	−0.736144	−	0.780267i	−0.0289632	−	0.0306992i
$647$	−25.9024			−1.01833			−0.509164	−	0.860670i	$-0.670045\pi$
$647$	−25.9024			−1.01833			−0.509164	+	0.860670i	$0.670045\pi$
$648$		0			0
$649$	2.34467			0.0920363
$650$	−1.47611	−	1.56458i	−0.0578977	−	0.0613680i
$651$		0			0
$652$	−0.216517	+	3.71746i	−0.00847947	+	0.145587i
$653$	−25.5536	+	2.98679i	−0.999991	+	0.116882i	−0.600306	−	0.799770i	$-0.704955\pi$
$653$	−25.5536	+	2.98679i	−0.999991	+	0.116882i	−0.399685	+	0.916653i	$0.630881\pi$
$654$		0			0
$655$	−19.0322	−	9.55834i	−0.743650	−	0.373475i
$656$	−16.6853	+	14.0006i	−0.651450	+	0.546631i
$657$		0			0
$658$	−7.86234	−	6.59728i	−0.306506	−	0.257189i
$659$	10.4490	+	24.2234i	0.407034	+	0.943610i	0.991248	+	0.132011i	$0.0421434\pi$
$659$	10.4490	+	24.2234i	0.407034	+	0.943610i	−0.584215	+	0.811599i	$0.698597\pi$
$660$		0			0
$661$	−27.2864	−	6.46701i	−1.06132	−	0.251537i	−0.337357	−	0.941377i	$-0.609533\pi$
$661$	−27.2864	−	6.46701i	−1.06132	−	0.251537i	−0.723962	+	0.689839i	$0.757681\pi$
$662$	1.85762	+	6.20489i	0.0721985	+	0.241160i
$663$		0			0
$664$	−20.2191	−	2.36328i	−0.784654	−	0.0917129i
$665$	2.98187	−	16.9110i	0.115632	−	0.655782i
$666$		0			0
$667$	3.03061	+	17.1874i	0.117346	+	0.665499i
$668$	0.849398	+	14.5836i	0.0328642	+	0.564257i
$669$		0			0
$670$	1.89981	−	4.40427i	0.0733963	−	0.170152i
$671$	−4.42525	+	2.22244i	−0.170835	+	0.0857964i
$672$		0			0
$673$	−36.1124	+	8.55879i	−1.39203	+	0.329917i	−0.857174	−	0.515027i	$-0.827782\pi$
$673$	−36.1124	+	8.55879i	−1.39203	+	0.329917i	−0.534855	+	0.844944i	$0.679634\pi$
$674$	2.01332	+	3.48718i	0.0775503	+	0.134321i
$675$		0			0
$676$	0.514578	−	0.891275i	0.0197915	−	0.0342798i
$677$	−0.454363	+	1.51768i	−0.0174626	+	0.0583291i	−0.966277	−	0.257506i	$-0.917099\pi$
$677$	−0.454363	+	1.51768i	−0.0174626	+	0.0583291i	0.948814	+	0.315835i	$0.102285\pi$
$678$		0			0
$679$	−27.6273	−	18.1707i	−1.06024	−	0.697329i
$680$	−3.66770	−	4.92657i	−0.140650	−	0.188925i
$681$		0			0
$682$	−0.837173	+	0.550617i	−0.0320570	+	0.0210842i
$683$	2.52567	+	0.919268i	0.0966420	+	0.0351748i	0.389889	−	0.920862i	$-0.372513\pi$
$683$	2.52567	+	0.919268i	0.0966420	+	0.0351748i	−0.293247	+	0.956037i	$0.594736\pi$
$684$		0			0
$685$	22.8025	−	8.29944i	0.871240	−	0.317105i
$686$	−0.497209	+	0.667868i	−0.0189835	+	0.0254993i
$687$		0			0
$688$	−23.8892	+	25.3211i	−0.910767	+	0.965357i
$689$	−33.3586	+	35.3581i	−1.27086	+	1.34704i
$690$		0			0
$691$	14.4189	−	19.3680i	0.548522	−	0.736793i	−0.438260	−	0.898848i	$-0.644405\pi$
$691$	14.4189	−	19.3680i	0.548522	−	0.736793i	0.986782	+	0.162056i	$0.0518124\pi$
$692$	10.8537	−	3.95044i	0.412598	−	0.150173i
$693$		0			0
$694$	−3.30945	−	1.20454i	−0.125625	−	0.0457237i
$695$	21.9647	−	14.4464i	0.833170	−	0.547985i
$696$		0			0
$697$	−7.38167	−	9.91530i	−0.279601	−	0.375569i
$698$	−2.03046	−	1.33546i	−0.0768541	−	0.0505477i
$699$		0			0
$700$	3.80916	−	12.7235i	0.143973	−	0.480902i
$701$	14.6288	−	25.3379i	0.552523	−	0.956998i	−0.445568	−	0.895248i	$-0.646998\pi$
$701$	14.6288	−	25.3379i	0.552523	−	0.956998i	0.998092	−	0.0617504i	$-0.0196683\pi$
$702$		0			0
$703$	4.75767	+	8.24053i	0.179439	+	0.310798i
$704$	−14.2667	+	3.38127i	−0.537697	+	0.127437i
$705$		0			0
$706$	0.729996	−	0.366618i	0.0274738	−	0.0137978i
$707$	−0.213411	+	0.494742i	−0.00802614	+	0.0186067i
$708$		0			0
$709$	−0.469838	−	8.06680i	−0.0176451	−	0.302955i	−0.995572	−	0.0940059i	$-0.970033\pi$
$709$	−0.469838	−	8.06680i	−0.0176451	−	0.302955i	0.977927	−	0.208949i	$-0.0670043\pi$
$710$	−0.906243	−	5.13956i	−0.0340107	−	0.192884i
$711$		0			0
$712$	−0.986786	+	5.59634i	−0.0369814	+	0.209732i
$713$	−11.0382	−	1.29019i	−0.413386	−	0.0483178i
$714$		0			0
$715$	−6.95880	−	23.2440i	−0.260244	−	0.869277i
$716$	5.12725	+	1.21518i	0.191614	+	0.0454134i
$717$		0			0
$718$	2.35665	+	5.46334i	0.0879495	+	0.203890i
$719$	24.5961	+	20.6385i	0.917278	+	0.769688i	0.973490	−	0.228731i	$-0.0734577\pi$
$719$	24.5961	+	20.6385i	0.917278	+	0.769688i	−0.0562116	+	0.998419i	$0.517902\pi$
$720$		0			0
$721$	−38.0482	+	31.9263i	−1.41699	+	1.18900i
$722$	−4.30822	−	2.16367i	−0.160335	−	0.0805235i
$723$		0			0
$724$	16.6969	−	1.95159i	0.620537	−	0.0725303i
$725$	−0.228532	+	3.92375i	−0.00848747	+	0.145724i
$726$		0			0
$727$	−11.1487	−	11.8170i	−0.413484	−	0.438268i	0.486838	−	0.873493i	$-0.338150\pi$
$727$	−11.1487	−	11.8170i	−0.413484	−	0.438268i	−0.900322	+	0.435225i	$0.856669\pi$
$728$	−15.9859			−0.592478
$729$		0			0
$730$	−5.29394			−0.195938
$731$	−13.5577	−	14.3704i	−0.501451	−	0.531507i
$732$		0			0
$733$	0.549456	−	9.43380i	0.0202946	−	0.348445i	−0.972841	−	0.231475i	$-0.925645\pi$
$733$	0.549456	−	9.43380i	0.0202946	−	0.348445i	0.993135	−	0.116970i	$-0.0373182\pi$
$734$	3.20060	−	0.374096i	0.118136	−	0.0138081i
$735$		0			0
$736$	26.1239	+	13.1199i	0.962938	+	0.483606i
$737$	11.4718	−	9.62596i	0.422568	−	0.354577i
$738$		0			0
$739$	−0.162054	−	0.135979i	−0.00596124	−	0.00500207i	0.639802	−	0.768540i	$-0.279016\pi$
$739$	−0.162054	−	0.135979i	−0.00596124	−	0.00500207i	−0.645763	+	0.763538i	$0.723461\pi$
$740$	10.5316	+	24.4150i	0.387150	+	0.897514i
$741$		0			0
$742$	14.2950	+	3.38797i	0.524785	+	0.124376i
$743$	−10.9870	−	36.6993i	−0.403076	−	1.34637i	−0.883130	−	0.469128i	$-0.844568\pi$
$743$	−10.9870	−	36.6993i	−0.403076	−	1.34637i	0.480054	−	0.877239i	$-0.340617\pi$
$744$		0			0
$745$	−4.29293	−	0.501772i	−0.157281	−	0.0183835i
$746$	−0.999215	+	5.66683i	−0.0365839	+	0.207477i
$747$		0			0
$748$	−1.62514	−	9.21664i	−0.0594211	−	0.336994i
$749$	0.179523	+	3.08229i	0.00655962	+	0.112624i
$750$		0			0
$751$	12.8067	−	29.6894i	0.467325	−	1.08338i	−0.507750	−	0.861504i	$-0.669523\pi$
$751$	12.8067	−	29.6894i	0.467325	−	1.08338i	0.975075	−	0.221876i	$-0.0712180\pi$
$752$	−28.4443	+	14.2853i	−1.03726	+	0.520930i
$753$		0			0
$754$	2.24663	−	0.532461i	0.0818175	−	0.0193911i
$755$	19.6111	+	33.9674i	0.713721	+	1.23620i
$756$		0			0
$757$	16.7349	−	28.9858i	0.608242	−	1.05351i	−0.383289	−	0.923629i	$-0.625209\pi$
$757$	16.7349	−	28.9858i	0.608242	−	1.05351i	0.991530	−	0.129877i	$-0.0414581\pi$
$758$	0.758841	−	2.53471i	0.0275623	−	0.0920646i
$759$		0			0
$760$	4.70364	+	3.09363i	0.170619	+	0.112218i
$761$	1.07825	+	1.44834i	0.0390865	+	0.0525023i	0.821237	−	0.570588i	$-0.193284\pi$
$761$	1.07825	+	1.44834i	0.0390865	+	0.0525023i	−0.782150	+	0.623090i	$0.785877\pi$
$762$		0			0
$763$	−14.7431	+	9.69669i	−0.533736	+	0.351044i
$764$	−3.31895	−	1.20800i	−0.120075	−	0.0437038i
$765$		0			0
$766$	−8.68571	+	3.16134i	−0.313827	+	0.114224i
$767$	2.05439	−	2.75952i	0.0741797	−	0.0996406i
$768$		0			0
$769$	23.3103	−	24.7075i	0.840593	−	0.890976i	−0.154693	−	0.987963i	$-0.549439\pi$
$769$	23.3103	−	24.7075i	0.840593	−	0.890976i	0.995286	+	0.0969864i	$0.0309203\pi$
$770$	−5.03207	+	5.33369i	−0.181343	+	0.192213i
$771$		0			0
$772$	−0.393653	+	0.528767i	−0.0141679	+	0.0190308i
$773$	0.0917313	−	0.0333874i	0.00329934	−	0.00120086i	−0.340370	−	0.940292i	$-0.610552\pi$
$773$	0.0917313	−	0.0333874i	0.00329934	−	0.00120086i	0.343669	+	0.939091i	$0.388330\pi$
$774$		0			0
$775$	−2.35185	−	0.856003i	−0.0844809	−	0.0307485i
$776$	9.05759	−	5.95727i	0.325149	−	0.213854i
$777$		0			0
$778$	−2.97061	−	3.99023i	−0.106502	−	0.143057i
$779$	9.46662	+	6.22630i	0.339177	+	0.223080i
$780$		0			0
$781$	4.67311	−	15.6093i	0.167217	−	0.558544i
$782$	−2.54026	+	4.39986i	−0.0908395	+	0.157339i

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.g (of order \(27\), degree \(18\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.209640 - 0.222205i) q^{2} +(0.110863 - 1.90345i) q^{4} +(-2.61158 + 0.305250i) q^{5} +(3.25303 + 1.63373i) q^{7} +(-0.914234 + 0.767134i) q^{8} +O(q^{10})\)	\(q+(-0.209640 - 0.222205i) q^{2} +(0.110863 - 1.90345i) q^{4} +(-2.61158 + 0.305250i) q^{5} +(3.25303 + 1.63373i) q^{7} +(-0.914234 + 0.767134i) q^{8} +(0.615319 + 0.516314i) q^{10} +(0.993292 + 2.30271i) q^{11} +(3.58046 + 0.848584i) q^{13} +(-0.318940 - 1.06533i) q^{14} +(-3.42545 - 0.400377i) q^{16} +(0.339876 - 1.92753i) q^{17} +(0.311537 + 1.76682i) q^{19} +(0.291500 + 5.00486i) q^{20} +(0.303440 - 0.703454i) q^{22} +(7.59313 - 3.81342i) q^{23} +(1.86197 - 0.441294i) q^{25} +(-0.562046 - 0.973492i) q^{26} +(3.47037 - 6.01086i) q^{28} +(-0.589089 + 1.96770i) q^{29} +(-1.09276 - 0.718719i) q^{31} +(2.05450 + 2.75967i) q^{32} +(-0.499558 + 0.328565i) q^{34} +(-8.99425 - 3.27364i) q^{35} +(4.98391 - 1.81400i) q^{37} +(0.327285 - 0.439620i) q^{38} +(2.15343 - 2.28250i) q^{40} +(4.33403 - 4.59381i) q^{41} +(6.02768 - 8.09658i) q^{43} +(4.49321 - 1.63540i) q^{44} +(-2.43918 - 0.887789i) q^{46} +(7.71104 - 5.07163i) q^{47} +(3.73300 + 5.01429i) q^{49} +(-0.488400 - 0.321226i) q^{50} +(2.01218 - 6.72114i) q^{52} +(-6.60535 + 11.4408i) q^{53} +(-3.29697 - 5.71052i) q^{55} +(-4.22732 + 1.00189i) q^{56} +(0.560728 - 0.281608i) q^{58} +(0.370314 - 0.858484i) q^{59} +(0.114814 + 1.97128i) q^{61} +(0.0693827 + 0.393489i) q^{62} +(-1.01524 + 5.75769i) q^{64} +(-9.60969 - 1.12321i) q^{65} +(-1.71264 - 5.72061i) q^{67} +(-3.63128 - 0.860629i) q^{68} +(1.15813 + 2.68485i) q^{70} +(-4.97716 - 4.17634i) q^{71} +(-5.04878 + 4.23643i) q^{73} +(-1.44790 - 0.727165i) q^{74} +(3.39758 - 0.397121i) q^{76} +(-0.530804 + 9.11355i) q^{77} +(7.97870 + 8.45693i) q^{79} +9.06806 q^{80} -1.92935 q^{82} +(11.7053 + 12.4069i) q^{83} +(-0.299234 + 5.13765i) q^{85} +(-3.06274 + 0.357983i) q^{86} +(-2.67459 - 1.34323i) q^{88} +(3.64757 - 3.06067i) q^{89} +(10.2610 + 8.60997i) q^{91} +(-6.41685 - 14.8759i) q^{92} +(-2.74348 - 0.650217i) q^{94} +(-1.35293 - 4.51909i) q^{95} +(-9.02241 - 1.05457i) q^{97} +(0.331615 - 1.88068i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8}+O(q^{10}) \) 144 * q - 9 * q^2 + 9 * q^4 - 9 * q^5 + 9 * q^7 + 18 * q^8	\( 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8} - 18 q^{10} - 9 q^{11} + 9 q^{13} - 9 q^{14} + 9 q^{16} + 18 q^{17} - 18 q^{19} + 63 q^{20} + 9 q^{22} - 36 q^{23} + 9 q^{25} - 45 q^{26} - 9 q^{28} + 45 q^{29} + 9 q^{31} - 63 q^{32} + 9 q^{34} - 9 q^{35} - 18 q^{37} + 9 q^{38} + 9 q^{40} + 27 q^{41} + 9 q^{43} - 54 q^{44} - 18 q^{46} - 63 q^{47} + 9 q^{49} + 225 q^{50} + 27 q^{52} - 45 q^{53} - 9 q^{55} - 99 q^{56} + 9 q^{58} + 117 q^{59} + 9 q^{61} - 81 q^{62} - 18 q^{64} - 81 q^{65} + 36 q^{67} + 18 q^{68} + 63 q^{70} + 90 q^{71} - 18 q^{73} - 81 q^{74} + 90 q^{76} - 81 q^{77} + 63 q^{79} + 288 q^{80} - 36 q^{82} - 45 q^{83} + 63 q^{85} - 81 q^{86} + 90 q^{88} + 81 q^{89} - 18 q^{91} + 63 q^{92} + 63 q^{94} - 153 q^{95} + 36 q^{97} - 81 q^{98}+O(q^{100}) \) 144 * q - 9 * q^2 + 9 * q^4 - 9 * q^5 + 9 * q^7 + 18 * q^8 - 18 * q^10 - 9 * q^11 + 9 * q^13 - 9 * q^14 + 9 * q^16 + 18 * q^17 - 18 * q^19 + 63 * q^20 + 9 * q^22 - 36 * q^23 + 9 * q^25 - 45 * q^26 - 9 * q^28 + 45 * q^29 + 9 * q^31 - 63 * q^32 + 9 * q^34 - 9 * q^35 - 18 * q^37 + 9 * q^38 + 9 * q^40 + 27 * q^41 + 9 * q^43 - 54 * q^44 - 18 * q^46 - 63 * q^47 + 9 * q^49 + 225 * q^50 + 27 * q^52 - 45 * q^53 - 9 * q^55 - 99 * q^56 + 9 * q^58 + 117 * q^59 + 9 * q^61 - 81 * q^62 - 18 * q^64 - 81 * q^65 + 36 * q^67 + 18 * q^68 + 63 * q^70 + 90 * q^71 - 18 * q^73 - 81 * q^74 + 90 * q^76 - 81 * q^77 + 63 * q^79 + 288 * q^80 - 36 * q^82 - 45 * q^83 + 63 * q^85 - 81 * q^86 + 90 * q^88 + 81 * q^89 - 18 * q^91 + 63 * q^92 + 63 * q^94 - 153 * q^95 + 36 * q^97 - 81 * q^98

Introduction

L-functions

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